Day 17: MHT-CET Maths

1. A.
   $\dfrac{1}{35}$
2. B.
   $\dfrac{11}{35}$
3. C.
   $\dfrac{2}{7}$
4. D.
   $\dfrac{1}{7}$

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1. A.
   $\left(0, -\dfrac{1}{2}, \dfrac{3}{2}\right)$
2. B.
   $(1, 0, 0)$
3. C.
   $\left(-\dfrac{1}{2}, 0, \dfrac{3}{2}\right)$
4. D.
   $\left(0, \dfrac{1}{2}, -\dfrac{3}{2}\right)$

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1. A.
   $x^2\left[\left(\dfrac{dy}{dx}\right)^2 + 1\right] = \left(\dfrac{dy}{dx}\right)^2$
2. B.
   $x^2\left[\left(\dfrac{dy}{dx}\right)^2 + 1\right] = -\left(\dfrac{dy}{dx}\right)^2$
3. C.
   $x^2\left[\left(\dfrac{dy}{dx}\right)^2 - 1\right] = -\left(\dfrac{dy}{dx}\right)^2$
4. D.
   $x^2\left[\left(\dfrac{dy}{dx}\right)^2 - 1\right] = \left(\dfrac{dy}{dx}\right)^2$

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1. A.
   $t$
2. B.
   $1$
3. C.
   $0$
4. D.
   $\dfrac{y}{x}$

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1. A.
   $\bar{r} = (2\hat{i} + 3\hat{j} - 2\hat{k}) + \lambda(\hat{i} - 2\hat{j} + \hat{k})$
2. B.
   $\bar{r} = (2\hat{i} - 3\hat{j} + 2\hat{k}) + \lambda(\hat{i} - 2\hat{j} + \hat{k})$
3. C.
   $\bar{r} = (2\hat{i} - 3\hat{j} - 2\hat{k}) + \lambda(\hat{i} - 2\hat{j} + \hat{k})$
4. D.
   $\bar{r} = (2\hat{i} + 3\hat{j} + 2\hat{k}) + \lambda(\hat{i} - 2\hat{j} + \hat{k})$

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